Зависает GUI во время выполнения функции

Если ваша программа завивает, значит какие-то выполняемые операции тяжелые и должны выполняться в дополнительном потоке. Как вариант, это может выглядеть примерно так:

import sys
import glob
from PIL import Image
from PyQt5 import QtCore, QtWidgets, QtGui
from PyQt5.Qt import *


class Ui_Program(object):
    def setupUi(self, Program):
        Program.setObjectName("Program")
        Program.resize(298, 99)
        self.centralwidget = QtWidgets.QWidget(Program)
        self.centralwidget.setObjectName("centralwidget")
        self.filePath = QtWidgets.QLineEdit(self.centralwidget)
        self.filePath.setGeometry(QtCore.QRect(10, 10, 281, 31))
        font = QtGui.QFont()
        font.setPointSize(10)
        font.setBold(True)
        font.setWeight(75)
        self.filePath.setFont(font)
        self.filePath.setStyleSheet("")
        self.filePath.setText("")
        self.filePath.setObjectName("filePath")
        self.convert = QtWidgets.QPushButton(self.centralwidget)
        self.convert.setGeometry(QtCore.QRect(30, 50, 241, 31))
        font = QtGui.QFont()
        font.setPointSize(14)
        self.convert.setFont(font)
        self.convert.setStyleSheet("QPushButton {\n"
"    border-style: outset;\n"
"    border: 1px solid gray;\n"
"    border-width: 1px;\n"
"    border-radius: 10px;\n"
"    background-color: rgb(227, 227, 227);\n"
"}\n"
"QPushButton:pressed {\n"
"    background-color: rgb(203, 203, 203);\n"
"}\n"
"")
        self.convert.setObjectName("btn")
        self.statusLabel = QtWidgets.QLabel(self.centralwidget)
        self.statusLabel.setGeometry(QtCore.QRect(10, 130, 241, 31))
        font = QtGui.QFont()
        font.setPointSize(14)
        self.statusLabel.setFont(font)
        self.statusLabel.setText("")
        self.statusLabel.setObjectName("statusLabel")
        Program.setCentralWidget(self.centralwidget)

        self.retranslateUi(Program)
        QtCore.QMetaObject.connectSlotsByName(Program)

    def retranslateUi(self, Program):
        _translate = QtCore.QCoreApplication.translate
        Program.setWindowTitle(_translate("Program", "MainWindow"))
        self.convert.setText(_translate("Program", "CONVERT"))


# +++ vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
class Thread(QtCore.QThread):  
    finished = QtCore.pyqtSignal()

    def __init__(self, parent=None):
        super().__init__(parent)
        self.file_path = None

    def run(self): 
        images = glob.glob(f"frames/*.jpg")
        images.sort()
        frames = [Image.open(image) for image in images]
        frame_one = frames[0]
        frame_one.save(
            f"{self.file_path}/example.gif", 
            format="GIF", 
            append_images=frames, 
            save_all=True, 
            duration=400, 
            loop=0
        )    
        self.finished.emit()
# +++ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^    

class MainWindow(QMainWindow, Ui_Program):
    def __init__(self):
        super(MainWindow, self).__init__()
        self.setupUi(self)
# ???        self.convert.clicked.connect(lambda: self.make_gif(self.filePath.text()))
        self.convert.clicked.connect(self.make_gif)  

        layout = QtWidgets.QVBoxLayout(self.centralwidget)
        layout.addWidget(self.filePath)  
        layout.addWidget(self.convert)
        layout.addWidget(self.statusLabel, alignment=Qt.AlignCenter)

        self.thread = Thread()                                         # +++
        self.thread.finished.connect(self._finished)                   # +++   

#    def make_gif(self, file_path):
    def make_gif(self):
        file_path = self.filePath.text()
        if not file_path:
            return

        self.thread.file_path = self.filePath.text()                   # +++
        self.thread.start()                                            # +++

        self.movie = QMovie("img/Fo2BxBK.gif")          # установмте какую-нибудь свою
        self.statusLabel.setMovie(self.movie)
        self.movie.start()

    def _finished(self):
        self.movie.stop()
        self.movie = QMovie(f"{self.filePath.text()}/example.gif")
        self.statusLabel.setMovie(self.movie)
        self.movie.setScaledSize(QSize(self.statusLabel.width(), self.statusLabel.height()))
        self.movie.start()    
        

if __name__ == '__main__':
    app = QApplication([])
    window = MainWindow()
    window.show()
    app.exec_()